Solve v^3*v*v^-6

$$v ^ { 3 } \cdot v \cdot v ^ { - 6 }$$

Evaluate

$$\frac{1}{v^{2}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$v^{3}v^{1}v^{-6}$$

Use the Multiplication Rule for Exponents.

$$v^{3+1-6}$$

Add the exponents 3 and 1.

$$v^{4-6}$$

Add the exponents 4 and -6.

$$v^{-2}$$

Differentiate w.r.t. v

$$-\frac{2}{v^{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{4}v^{-6})$$

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{-2})$$

The derivative of ax^{n} is nax^{n-1}.

$$-2v^{-2-1}$$

Subtract 1 from -2.

$$-2v^{-3}$$